Star configuration optical resonator

ABSTRACT

This work presents a concept and scaling considerations for a diode-pumped solid-state laser operating in the active mirror mode. The laser uses relatively thin gain medium with large aperture that is pressured-clamped onto a transparent substrate with an internal microchannel type heat exchanger. Pump radiation is injected through the transparent substrate into the back face of the gain medium. Effective radiation of transverse temperature gradients makes this laser suitable for operation at high-average power while delivering good beam quality. Keywords: solid-state lasers, active mirror, thin disk laser, beam quality

1. INTRODUCTION

Optical pumping generates a large amount of heat within the solid-state laser (SSL) medium and increases its temperature. Continuous operation of the laser, therefore, requires removal of the waste heat by cooling selected surfaces of the laser medium. Because SSL media typically have a low thermal conductivity, a significant thermal gradient is created between the hot interior and the cooled outer surfaces. This causes a gradient in the index of refraction, mechanical stresses, depolarization, detuning, and other effects, with likely consequences of degraded beam quality, reduced laser power, and possibly a fracture of the SSL medium [1]. Such effects present a major challenge to scaling of SSL to high-average power (HAP). Pumping by laser diodes, which was introduced in the last decade greatly reduces the amount of waste heat and paves the way for development of HAP-SSL with good beam quality.

It has been recognized that optical distortions caused by transverse gradients (i.e., ⊥ to laser beam axis) degrade beam quality. Transverse temperature gradients (∇⊥T) can be reduced by injecting the pump radiation into the laser gain medium and extracting waste heat in a direction parallel to laser beam axis. A class of SSL known as “active mirror amplifies” (AMA) has effectively used this technique and demonstrated generation of laser output with very good beam quality [2,3]. In the classical AMA concept originated in the late 1960's, a large aspect ratio, edge-suspended, Nd:Glass disk (or slab) several centimeter-thick, is pumped by flashlamps and cooled by liquid on the back face. However, this device is not suitable for operation at HAP because of poor heat removal and resulting thermomechanical distortion of the edge-suspended disk. Previous attempts to mitigate these problems and increase the average power output of AMA, were met with encouraging but limited results [4,5]. In recent years, the AMA concept has been a revived in Germany in the form of a “thin disk laser” (TDL) [6]. The thin disk laser uses a gain medium disk with several mm in diameter and 200-400 μm in thickness soldered to a heat sink. Diode-pumped Yb:YAG thin disk laser has demonstrated laser outputs approaching 1 kW of average power with beam quality M²˜12 [7]. Another variant of the thin disk laser intended for ultra-HAP outputs is being investigated at the Lawrence Livermore National Library [8].

In our recent publication, we introduced a new AMA concept, which shows a strong potential for sealing to HAP [9]. In this work, we will further elaborate on this concept, develop basic scaling relationships, and present results of preliminary analyses.

2. ACTIVE MIRROR AMPLIFIER FOR HAP

We are investigating the feasibility of several AMA concepts for scaling to HAP. One concept uses a large aperture laser gain medium mounted on a rigid, cooled, and optically transparent substrate, FIG. 1. The laser medium is a relatively thin disk made of Nd:YAG, Nd:GGG, or Nd:Glass about 2.5 mm in thickness and with a diameter typically between 5 and 15 cm. Note that the disk thickness in this AMA concept is about 10 times less than in the classical AMA and about 10 times more than in the thin disk laser. As in the classical AMA, both faces of the disk have dichroic coatings; the front face coating is antireflective at laser wavelength and reflective at pump wavelength, and the rear surface coating has the opposite properties.

The substrate is made of material optically transparent at pump diode wavelength and it is designed to be very rigid. In addition, the substrate contains a built-in heat exchanger with microchannels on the front surface so that coolant can directly wet the back face of the laser medium disk. Except for the microchannel penetrations the front surface (facing the disk) of the substrate is ground to optical flatness. Such substrate can be constructed by diffusion bonding of several plates of optical glass or crystal as, for example, previously used by Boeing for liquid-cooled laser mirrors and windows [10]. The disk is attached to the substrate by a hydrostatic pressure differential between the surrounding atmosphere and the coolant fluid in the microchannels. This novel approach permits thermal expansion of the laser medium disk in the transverse direction while maintaining a thermally loaded disk in a flat condition. In addition, the disk can be pre-formed to reduce the required clamping pressure [11].

Collimated pump diode radiation is injected into the disk through the optically transparent substrate and the heat exchanger. Close proximity of the diodes to the disk makes it possible to realize good transport efficiency and pump uniformity. Host material of the disk is doped with lasant ions so that most of the pump power is absorbed in two passes through the laser medium. Perimeter of the disk has cladding for absorption of amplified spontaneous emission (ASE). Optical contact between the disk and the substrate provides an effective seal between the coolant and high-pressure atmosphere in which the AMA is immersed. In addition, a backup elastomeric seal is provided along the perimeter of the disk. Coolant in the heat exchanger is chosen to avoid excessive pump losses by absorption and scattering. If necessary, pump diode intensity may be varied across the aperture to compensate for gain saturation.

3. THERMOMECHANICAL EFFECTS IN AMA

Consider an AMA disk of diameter d and thickness L attached to a heat sink, as shown in FIG. 2. Rough estimates of thermomechanical effects in AMA disk can be derived along the same lines as the corresponding analysis for the zigzag slab laser (e.g., see reference [12]) with the disk being represented by a semi-infinite slab with internal heating. We assume for a moment that the thermal conductivity κ of the laser medium is temperature invariant and the (time averaged) volumetric heating Q is spatially uniform. Then, the temperature profile (normal to disk face) is parabolic with the front-to-back face temperature rise ΔT_(FTB)=QL²/(2κ). To verify that the spatially uniform heating approximation is reasonable, we conducted a more accurate analysis of temperature distribution in the disk which took into account a realistic power deposition profile as well as temperature dependence of κ. Typical power density profile for a 90% absorption in two passes in a 2.5 mm-thick Nd:YAG disk is shown in FIG. 3. Temperature dependence of K was approximated as κ(T)=44.971 T^(−1.2272), which is an exponential curve fit onto data in reference [1]. We used this heat load distribution as an input to a one-dimensional finite-element model which calculated the temperature profile in the direction normal to disk face. Results of this simulation shown in FIG. 4 indicate that the temperature profile based on nonuniform beat load and temperature dependent κ is still very closely parabolic, which validates our approximation.

As in the slab laser, the limiting thermal stress in AMA is tensile stress σ_(s) on the cooled face of the laser medium. In particular, this stress is given by σ_(s)=(2/3)γE ΔT_(FTB)/(1−ν), where γ is the coefficient of thermal expansion, E is Young's modulus, and ν is the Poisson ratio. Consistent with the conventions, we define the thermal stress resistance parameter as

=κ(1−ν)σ_(s,fract)/(γE), where σ_(s,fract) is the surface stress at fracture [1]. We observe that ΔT _(FTB,fract)=(3/2)

κ  (1)

Thus the volumetric heat load for safe operation limited by design stress σ_(s,max) is Q _(max)=3

b/L ²  (2) where the stress factor b is the ratio of the design tensile stress and the fracture stress on the cooled surface (i.e., b=σ_(s,max)/σ_(s,fract)). Front-to-back temperature distribution in the disk produces a stress profile that tends to “dish bead” (bulge) the laser medium disk away from the substrate. The pressure differential between the surrounding atmosphere and the coolant on the back side of the disk must be sufficient to overcome this tendency, keep the disk in flat condition and attached to the substrate. By comparing disk deflections caused by distributed load to those caused by thermal stresses (e.g., see reference [13]) we derived the following expression for the pressure differential Δp_(clamp) required to maintain the disk of diameter d and thickness L in flat condition: Δp _(clamp)=(32/3) (L/d)² EγΔT _(FTB)/[(1−ν)(5+ν)]  (3)

In the regime limited by thermal fracture, ΔT_(FTB) is given by e.g. (1) and the corresponding Δp_(clamp) can be expressed as Δp _(clamp)=16(L/d)² bσ _(s,fract)/(5+ν)  (4)

FIG. 5 shows scaling of Δp_(clamp) as a function of d/L predicted by e.g. (4) for several SSL host materials. In most cases of practical interest, Δp_(clamp) is less than 100 psi. To evaluate the flatness of pressure-clamped, thermally loaded disk, we conducted 2-dimensional numerical simulations using the ALGOR®^(a) finite element model. FIG. 6 shows a result of such computer simulations for a GGG crystal indicating that a thermally loaded disk can be maintained flat to within λ/20 over 80% of the diameter with only a modest Δp_(clamp). Pre-forming the disk to a shape opposite to anticipated deflection can significantly reduce required Δp_(clamp) [11]. ^(a) Algor Systems, Pittsburgh, Pa., USA

4. ELEMENTARY SCALING THEORY

AMA designer must reconcile various conflicting engineering requirements and physical trends such as those shown in FIG. 7. For example, to increase the average laser power, it seems desirable to make the aperture size as large as practically possible and pump it intensely. However, the aperture size is constrained both by manufacturing limitations and by ASE losses, which are favored by the resulting combination of high gain and long ray path (∝ disk diameter). Increased pumping also increases thermal load, which in turn limits the AMA thickness.

From a system point of view, an ideal AMA would generate high-average power output with good BQ and acceptable round-trip gain. In an attempt to achieve this goal, the designer will soon discover that for any given choice of AMA diameter and thickness, the laser output will be limited by ASE and thermal fracture. To uncover the scaling relationships, we will consider an AMA operating in this limiting regime. Other (but softer) constraints include heat sink capacity, and producible crystal size. Our objective is to develop first-order scaling laws that show the interplay of key parameters, rather than precise formulas for prediction of absolute performance.

To arrive at a closed-form result, we will make several simplifying assumptions. In particular, we will assume that 1) pump power is uniform throughout the gain medium volume, 2) thermomechanical properties of the gain medium do not vary significantly over the temperature range within the disk, 3) heat is uniformly extracted from the cooled surface, and 4) and parasitic oscillations are effectively suppressed. The last item means that ASE rays are largely absorbed at the AMA disk perimeter. We will also assume that the AMA is pumped with long pulses and lases in a quasi-cw mode (rather than storage mode). In addition, the pulse spacing is much shorter than the thermal dissipation time of the laser gain medium given by c_(p) ρL²/κ, where ρ and c_(p) are respectively the density and heat capacity of the gain medium. We will see that for any choice of AMA disk diameter, ASE loss considerations limit the pump intensity and for any choice of disk thickness, thermal fracture considerations limit the pulse duty factor. Note that it is not necessary to assume any specific pumping architecture. The derivations are shown for a 4-level laser but the same logic can be used to derive scaling laws for quasi-3 level lasants such as Yb³⁺.

Consider an AMA of diameter d. To obtain the highest (instantaneous) laser power the AMA is pumped to its ASE “limit,” i.e., a point beyond which ASE losses are not acceptable. This condition defines the maximum (i.e., ASE-limited) small-signal gain g_(o,ASE) in accordance with the ASE criterion g _(o,ASE) d _(ASE)=φ  (5) where the ASH parameter φ depends on gain medium geometry and mode of operation. For example, φ=2.5 is often taken as a limit for a q-switched laser [14, 15]. ASH losses are far less severe for cw and quasi-cw lasers where the gain is clamped, hence φ=3.5 seems to be a conservative limit. In a 4-level laser system the volumetric density of absorbed pump power p_(a) required to produce the gain g_(o,ASE) is p _(a,ASE) =g _(o,ASE) I _(sat)η_(u) ⁻¹  (6) where I_(sat) is the saturation intensity and η_(u) is the upper state efficiency (product of Stokes and quantum efficiencies). The corresponding time-averaged volumetric heat load is Q=p _(a,ASE)ψ_(d) f _(h)  (7) where ψ_(d) is the pump duty factor (=pump pulse length multiplied by pulse frequency) and f_(h) is the heat fraction (=heat induced/absorbed pump energy). The maximum duty factor ψ_(d,max) corresponds to the point where the laser gain medium has reached its maximum design stress σ_(s,max)=bσ_(s,fract). This is where the heat load attains its maximum design value Q_(max) given by eq. (2). By combining eq.'s (2, 5, 6, and 7) we obtain the disk thickness L_(max) corresponding to the maximum design thermal and stress loads L _(max)=(3bη _(u) d _(ASE))^(1/2)(I _(sat)ψ_(d,max) φf _(h))^(−1/2)  (8)

Under the noted pump conditions, a value of L greater than L_(max) would result in exceeding the design and stress loads. Recall that the average laser power available for outcoupling is P_(avail,avg)=Vp_(a)η_(u)ψ_(d), where V is the volume of the gain medium. In an AMA operating in the regime limited by ASH and fracture, the volume is given by V=(π/4) d_(ASE) ²L_(max). Hence, the maximum available average laser power P_(avail,avg,max) can be expressed as P _(avail,avg,max)=(π/4)(3bη _(u) I _(sat)ψ_(d,max) φd _(ASE) ³ f _(h) ⁻¹)^(1/2)  (9)

It is interesting to note that when designing an ASE/fracture-limited AMA with a certain target laser power, apart from choosing the gain medium the designer is left with only three control parameters: ψ_(d), b, and d. As an example, FIGS. 8, 9 and 10 show the scaling of disk thickness L_(max), maximum average available power P_(avail,avg,max), round-trip gain 2g_(o,ASE)L_(max) (at normal incidence), and heat sink load q_(max)=Q_(max)L_(max) for AMA disks using Nd:YAG, Nd:GGG, and Nd:Glass. In each case the AMA is operated in a ASE/fracture-limited regime with b=0.5 and ψ_(d,max)=25%, except the last case where ψ_(d,max)=5%. Intuitive explanation of the trends shown in these figures is as follows: As the disk diameter d increases, pump density p_(a) (∝d⁻¹) must be scaled back to avoid excessive ASH losses. This causes a reduction in heat load Q (∝d⁻¹), which in turn permits increasing the disk thickness L (∝Q^(−1/2)) and results in an increase of disk volume (∝d^(5/2)). Since P_(avail,avg) scales linearly with volume and pump density, its scaling with d^(3/2) is justified. The round trip gain vanes linearly with p_(a) and L, which explains its dependence on d^(−1/2).

In practice, one has to consider the pumping architecture and pump absorption in the laser gain medium. For example, doping limit of Nd³⁺ in YAG is ˜1.5% atomic, which means that a face-pumped AMA with 2-pass absorption at 90% efficiency (as shown in FIG. 3) should have about 2.5-mm thickness. FIG. 8 indicates that a 2.7-mm thick AMA disk corresponds to a 5-cm diameter. Such a disk would generate P_(avail,avg,max)=2.7 kW with ˜38% round-trip small-signal gain (2g_(o)L) at normal incidence. Observe that heat exchanger load q is only 61 W/cm². The 5-cm diameter disk could be regarded as the manufacturing limit. Disk diameters smaller than 5 cm would have a correspondingly smaller thickness. If the 1.5% at. doping limit of Nd³⁺ in YAG cannot be exceeded, this would result in less efficient pump absorption efficiency. For disks with very small diameter (and, therefore, small thickness) such reduction in pump absorption must be compensated by reinjection of unabsorbed pump power as it is often practiced for certain thin disk laser concepts [16, 17].

Doping limit of Nd³⁺ in GGG is about 2.5% at., which means that a 2-pass absorption with 90% efficiency could be obtained in a disk with thickness at least 1.5 mm. FIG. 9 shows that a GGG disk with 15-cm diameter (which could be regarded as the manufacturing limit) and 2.4-nim thickness would generate P_(avail,avg,max)=14.9 kW with ˜11% round-trip small-signal gain. The corresponding heat exchanger load q is only 37 W/cm². Nd:Glass is also suitable for a face-pumped AMA. While its pump cross-section is about three times lower than that for Nd:YAG, glass can be doped with Nd³⁺ ions up to about 4.5% at. At this doping level a face-pumped Nd:Glass AMA disk would be about 2.5 mm thick for a 2-pass absorption with 90% efficiency. Glass host material has the obvious advantage of being available in large size and at relatively low cost, but at least some of this is offset by its low emission cross-section and poor thermal conductivity.

5. IMPLICATIONS ON BEAM QUALITY

So far we have assumed that the heat flow throughout the AMA disk was perpendicular to the cooled face. While this is a reasonable approximation for the purposes of basic thermomechanical analysis, small transverse temperature gradients (∇⊥T) due to finite dimensions of the disk and the mnicrochannels affect local optical path and distort the phase front of the incident laser beam. A two-dimensional analysis we conducted using the ANSYS®^(b) finite-element model revealed two areas of the AMA where ∇⊥T may affect optical path difference (OPD), FIG. 11. The first one is near the edge of the disk where pump power and laser extraction are abruptly cut off. We are now investigating several techniques to mitigate this effect. The second area is near the back face of the disk, where the disk surface facing the microchannel experiences higher heat transfer than the surface contacting the substrate material. Such variations in heat extraction generate small local perturbations to the otherwise flat isotherms. This effects reaches to a depth that is approximately equal to the width of the microchannels. We have shown that reducing the microchannels to <0.25 mm width brings the OPD to tolerable level, FIG. 12. There are other, more subtle effects that can potentially affect beam quality, for example, a less-than-perfectly uniform gain profile due spatial inhomogenieties of the pump arrays. Addressing this topic is, however, beyond the scope of this article. ^(b) Ansys, Inc., South Pointe, Pa.

6. DESIGN EXAMPLE

The face-pumped AMA concept for HAP is very conducive to integration into compact, selfcontained modules. An illustrative example of such a module is shown in FIG. 13. An AMA gain medium disk with ASE absorbers around the perimeter is pressure-clamped onto a rigid, optically transparent substrate containing a liquid-cooled microchannel heat exchanger. Several holders placed around the perimeter of the AMA disk are intended to maintain the disk in place when the hydrostatic clamp pressure is removed. Arrays of laser diodes mounted on a coolant manifold inject pump radiation through the transparent substrate. Optical alignment is facilitated by adjusting the position of the substrate. A laser amplifier or regenerative oscillator may use 10 or more such modules to obtain a desired gain. In an oscillator, the gain must be sufficient for high outcoupling from an unstable resonator of suitable configuration as shown, for example, in FIG. 14.

Consider a laser with unstable resonator such as in FIG. 14 using 10 identical AMA modules each containing a Nd:YAG AMA disk with a 5-cm diameter (4.5-cm diameter useful aperture) and 2.5-mm thickness. The disks are doped for 90% pump absorption, which results in the power absorption profiles shown in FIG. 3. When the system is operated in the regime limited by ASE and thermal fracture with pump duty factor ψ_(d)=0.24 and stress factor b=0.5, each module would generate about 2.2 kW of average laser power available for extraction. The round-trip small-signal gain for all 10 modules is about 6.8, which justifies use of unstable resonator with high outcoupling. Using a simple solid-state laser oscillator model we calculated that with 35% outcoupling 77% of available laser power can be extracted from the system. This translates to 14.5 kW of output laser power at about 49% optical-to-optical efficiency.

7. COMMERCIAL APPLICATIONS FOR HAP SSL

Market for lasers used in materials processing approached $1.1 billion in 1999 and is expected to grow by 14% in 2000 [18]. In addition to this very strong market, availability of multi-kilowatt SSL with good beam quality is expected to open the door to new industrial applications in laser material processing. One of the emerging applications is precision laser machining (PLM) which utilizes high-brightness laser beams to make deep-penetration welds and clean cuts with only very small beat-affected zone [19]. Intense, short-wavelength, highly-focused laser beams are also beneficial for cutting and welding of aluminum in manufacture of automotive bodies [20] and commercial aircraft [21]. Encouraged by recent laboratory demonstrations [22], rock drilling by ultra-HAP lasers is now seriously considered by the gas and petroleum industry [23]. This application would require a 100 kW-class average power beam delivered to a drill head through optical fiber(s). Similar requirements are also projected for laser-assisted dismantlement of nuclear reactors where metal components up to 12 inches in thickness must be remotely cut in a high radiation environment [24].

8. CONCLUSION

We presented a concept and scaling considerations for a large aperture, face-pumped AMA suitable for operation at HAP while delivering good beam quality. AMA gain medium thickness and doping are chosen so that pump diode radiation is absorbed in two passes and waste heat can be efficiently extracted. The AMA can be used as a gain element in a wide variety of laser oscillator and power amplifier configurations.

ACKNOWLEDGEMENTS

Author is indebted to the following people at The Boeing Company: Charlie Turner Jr. for many useful discussions, Jack Carroll for performing thermal analysis of the AMA disk using the ANSYS® model, and James Moldenhauer for performing stress analysis using the ALGOR® model.

REFERENCES

-   1. W. Koechner, “Solid-state laser engineering,” Chapter 7:     Thermo-optic effects and heat removal, 5^(th) edition, Springer     Verlag, Berlin, 1999 -   2. J. A. Abate, L. Lund, D. Brown, S. Jacobs, S. Refermat, J.     Kelly, M. Gavin, J. Waldbillig, and O. Lewis, “Active mirror: a     large-aperture medium-repetition rate Nd:Glass amplifier,” Appl.     Opt. Vol. 20, no. 2, 351, 1981 -   3. D. C. Brown, J-H. Kelly, and J. A. Abate, “Active-mirror     amplifiers: Progress and prospects,” IEEE J. of Quantum Electron.,     vol. 17, no. 9, 1755, 1981 -   4. D. C. Brown, R. Bowman, J. Kuper, K. K. Lee, and J. Menders,     “High-average power active-mirror amplifier,” Applied Optics, vol.     25, no. 5, pp. 612-618, Mar. 1, 1986 -   5. J. H. Kelly, D. L. Smith, J. C. Lee, S. D. Jacobs, D. J.     Smith, J. C. Lambropoulos, and M. J. Shoup III, “High-repetition     rate Cr:Nd:GSGG active mirror amplifier,” Optics Letters, vol. 12,     no. 12, pp. 996-998, 1987 -   6. A. Giesen, H. Hugel, A. Voss, K. Wittig, U. Branch, and H.     Opower, “Scalable concept for diode-pumped high-power lasers,” Appl.     Phys. B 58, 365-372, 1994 -   7. C. Stewen, K. Contag, M. Larionov, A. Giesen, and H. Hugel, “1-kW     CW thin disk laser,” IEEE J. Selected Topics in Quantum Electr.,     vol. 6, no. 4, pp. 650-657, July/August 2000 -   8. L. Zapata, R. Beach and S. Payne, “Composite thin-disk laser     scalable to 100 kW average power output and beyond”, in the     Technical Digest from the Solid State and Diode Laser Technology     Review, held in Albuquerque, N. Mex., Jun. 5-8, 2000 -   9. J. Vetrovec, “Diode-pumped active mirror amplifier for     high-average power,” in proc. from LASER 2000 Conference held in     Albuquerque, N. Mex., Dec. 4-8, 2000 -   10. M. A. Culpepper, J. P. Metz, and J. L. Stapp, “Liquid-cooled     transmissive optical component,” in the Technical Digest from the     Solid State and Diode Laser Technology Review held in     Albuquerque, N. Mex., Jun. 5-8, 2000 -   11. J. Vetrovec, U.S. patent application Ser. No. 09/505,399 -   12. J. M. Eggleston, T. J. Kane, K. Kuhn, J. Unternanrere, and R. L.     Byer, “The slab geometry laser—Part 1: Theory,” IEEE J. of Quantum     Electron., vol. 20, no. 3, March 1984 -   13. R. J. Roark and W. C. Yound, “Formulas for Stress and Strain,”     5^(th) edition, Chapter 10: Flat Plates, McGraw-Hill Book Co., New     York, N.Y., 1975 -   14. D. C. Brown, D. P. Benfey, W. J. Gelu, D. H. Holmes, and K. K.     Lee, “Parasitic oscillations and amplified spontaneous emission in     face-pumped total internal reflection lasers,” in Proc. SPIE, vol.     736, 1987, pp. 74-83 -   15. N. P. Barnes and B. M. Walsh, “Amplified Spontaneious     Emission—Application to Nd:YAG lasers,” IEEE J. of Quantum     Electron., vol 35, no. 1, January 1999, pp. 101-109 -   16. I. Johansen, S. Erhard, D. Muller, C. Stewen, A. Gieseti, K.     Contag, “Nd:YAG thin disk laser,” in Proc. from Advanced Solid-State     Lasers 2000, H. Injeyan, U. Keller and C. Marshal (eds.) Optical     Society of America, Washington, D.C., February 2000 -   17. S. Erbart, M Karszewski, C. Stewen, A. Giesen, K. Contag, and V.     Voss, “Pumping schemes for multi-kW thin disk lasers,” in Proc. from     Advanced Solid-State Lasers 2000, H. Injeyan, U. Keller and C.     Marshal (eds.) Optical Society of America, Washington, D.C.,     February 2000 -   18. S. G. Anderson, “Review and forecasts of laser markets, Part 1:     Nondiode lasers,” Laser Focus World, pp. 92-112, January 2000 -   19. J. Machan et al., “High-brightness, 3 kW diode-pumped,     industrial laser,” in Proc. from ICALEO'1999, San Diego, Calif.,     Nov. 15-18, 1999, 143-148 -   20. W. Penn, J. Clarke, and E. Quinn, “High speed laser blanking of     aluminum,” to be published in Proc. from ICALEO'2000, Dearborn,     Mich., Oct. 2-5, 2000 -   21. “Easier and quicker,” Aerospace, Daimler-Benz Aerospace Airbus     GmbH, Hamburg, Germany, 1^(st) quarter, 2000 -   22. D. G. O'Brien, R. M. Graves, and E. A. O'Brien, “StarWars laser     technology for gas drilling and completions in the 21^(st) century,”     in Proc. from the 1999 annual Technical Conference and Exhibition of     the Society of Petroleum Engineers (SPE) in Houston, Tex.; SPE     Intl., Richardson, Tex. -   23. M. R. Hallada, R. F. Walter, and S. L. Seifert, “Rock excavation     using COIL,” to be published in Proc. from LASERS 2000,     Albuquerque, N. Mex., Dec. 4-8, 2000 -   24. J. Vetrovec, M. Hallada, S. Seifert, and R. Walter, “Chemical     oxygen-iodine laser for dismatlement of nuclear reactors,” in Proc.     from ICALEO 1999, pp. 124-133 

1. A linear optical resonator, comprising: an optical cavity, for amplifying laser radiation; and a plurality of optical elements disposed in a circumferential array along the perimeter of said cavity, each in an allocated one of a plurality of substantially equally spaced perimeter segments, and each cooperatively aligned to receive and transmit laser radiation through said cavity along a propagation path substantially in the form of a star polygon.
 2. The linear optical resonator of claim 1, where the laser radiation is transmitted through said cavity at a cavity wavelength.
 3. The linear optical resonator of claim 2, wherein each of said plurality of optical elements is positioned in said circumferential array at an associated one of a like plurality of vertices of said star polygon laser propagation path.
 4. The linear optical resonator of claim 1, wherein said circumferential array of said plurality of optical elements comprises an outcoupler, an end mirror, and one or more active mirror amplifier (AMA) modules, each of said plurality of elements being positioned along the cavity perimeter at an associated one of a like plurality of vertices of said star polygon laser propagation path, said outcoupler and said end mirror being positioned at terminal vertices of said star polygon propagation path for circulating the laser radiation therebetween, and said AMA modules being arranged in operating relationship to one another at vertices intermediate thereto for amplifying the laser radiation cycling between said outcoupler and said end mirror.
 5. The linear optical resonator of claim 4, wherein said plurality of optical elements further include a highly reflective mirror which is cooperatively aligned in said circumferential array to exchange laser radiation between said outcoupler and said AMA modules.
 6. The linear optical resonator of claim 4 wherein the sum number of said plurality of optical elements is a prime number.
 7. The linear optical resonator of claim 6, wherein each said AMA module includes at least one, actively cooled solid-state laser gain medium arranged in an active mirror configuration, and a pump for providing optical pump radiation into said laser gain medium for excitation thereof.
 8. The linear optical resonator of claim 6, wherein: said prime number is N; and each of said N number of optical elements are aligned in said circumferential array to exchange laser radiation with first and second others of said N number of elements which are positioned X number of said perimeter segments clockwise and counterclockwise, respectively, therefrom in said circumferential array, said N and X numbers being relatively prime numbers, and said laser propagation path being substantially in the form of an {N, X} star polygon.
 9. The linear optical resonator of claim 8, where X=(N−1)/2.
 10. The linear optical resonator of claim 9, where N=11 and X=5.
 11. The linear optical resonator of claim 10, wherein said optical cavity is unstable.
 12. A linear optical resonator, comprising: an optical cavity, for amplifying laser radiation; and N number of optical elements, including an outcoupler, an end mirror, and one or more active mirror amplifier (AMA) modules, disposed in a circumferential array at substantially equal spaced intervals along the perimeter of said cavity, each of said N number of elements being positioned and cooperatively aligned therein to exchange laser radiation with first and second others of said N number of elements which are positioned X number of said perimeter segments clockwise and counterclockwise, respectively, therefrom in said circumferential array, said N number and said X number being relatively prime numbers, whereby said N number of optical elements circulate laser radiation through said cavity along a propagation path substantially in the form of an {N, X} star polygon.
 13. The linear optical resonator of claim 12, where X=(N−1)/2.
 14. The linear optical resonator of claim 13, where N=11 and X=5.
 15. The linear optical resonator of claim 14, wherein said optical cavity is unstable.
 16. The linear optical resonator of claim 14, wherein said plurality of optical elements further includes a highly reflective mirror which is cooperatively aligned in said circumferential array to exchange laser radiation between said outcoupler and said AMA modules.
 17. The linear optical resonator of claim 12, wherein each said AMA module includes at least one, actively cooled solid-state laser gain medium arranged in an active mirror configuration, and a pump for providing optical pump radiation into said laser gain medium for excitation thereof.
 18. A linear optical resonator, comprising: an optical cavity, for amplifying laser radiation; and a plurality of optical elements arranged in two or more groups, including at least a first group and a last group, each having N number of optical elements, said first group including an outcoupler and one or more active mirror amplifier (AMA) modules and said last group including an end mirror and one or more AMA modules, said N number of elements in each group being disposed in a planar circumferential array, in a group common tier, in substantially equal perimeter segments of said cavity, said N optical elements of each group being cooperatively aligned within their group common tier to exchange laser radiation with first and second others of said N number of elements that are positioned X number of said perimeter segments clockwise and counterclockwise, respectively, therefrom in said group common tier, said N number and said X number being relatively prime numbers, whereby laser radiation is circulated within each said group common tier along a propagation path substantially in the form of an {N, X} star polygon; wherein: at least one of said AMA modules in each said group common tiers being aligned out of the plane of its circumferential array to exchange laser radiation with another AMA in another group common tier, whereby amplification of the laser radiation within said optical cavity occurs with circulation of the laser energy through the AMA modules of each of the common group tiers.
 19. The linear optical resonator of claim 18, wherein each said AMA module includes at least one, actively cooled solid-state laser gain medium arranged in an active mirror configuration, and a pump for providing optical pump radiation into said laser gain medium for excitation thereof.
 20. The linear optical resonator of claim 18, where X=(N−1)/2.
 21. A method of amplifying laser energy in an optical resonator, comprising: providing an optical cavity, for amplifying laser radiation; and disposing a plurality of optical elements in a circumferential array along the perimeter of said cavity, each in an allocated one of a plurality of substantially equally spaced perimeter segments, and each cooperatively aligned to receive and transmit laser radiation through said cavity along a propagation path substantially in the form of a star polygon. 